Updated as of Megabonk version 1.0.7.

Weapon upgrades will randomly select from a list of possible buffs. Common-rarity upgrades will buff one or two stats, but all higher-rarity upgrades will buff two of the weapon's stats. The buff's effectiveness is unaffected by how many buffs the upgrade contains, so a weapon upgrade with only one buff may be particularly undesirable.

Tomes can only buff a single stat, so their upgrades will contain only one buff regardless of rarity. Tome upgrades apply to the character and therefore affect all weapons, while weapon upgrades apply only to the associated weapon. Upgrades are additive, but when both the weapon and the character buff the same stat, the effect can be multiplicative for some stats (such as Size) but additive for others (such as Projectile Count).

The effect of rarity on buff values is summarized in the table below:


For example, Sword upgrades can have the following buffs:


The buff factor may vary due to rounding. It is presently not known whether the rounded values are used only for display or for calculation as well.

This section lists all of the stats that each weapon's upgrades may include. If a weapon only has two upgradable stats, like Aura's damage and size, then every non-common upgrade will buff both stats. In comparison, the Revolver's upgrades will randomly select two of the six upgradable stats to buff, so care should be taken when choosing which upgrade to pick.

In the tables below, the base upgrade value is the buff received from common-rarity upgrades.

Tomes modify the character's stats. See the next section for characters' initial values.

This table shows typical initial values for character stats, and the tables below detail how various characters deviate from the standard.

Suppose you are given a choice between any common Revolver upgrade. Which upgrade will increase your DPS the most?

To answer this question, we first need an equation to show how DPS depends on the Revolver's stats. Revolver upgrades can improve Damage, Projectile Count, Projectile Bounces, Crit Chance, Crit Damage, and Projectile Speed. We can ignore Projectile Speed since it doesn't affect DPS. In broad strokes, we have that:

• DPS = k * Damage * Projectile Count * (1 + Projectile Bounces) * (1 + Crit factor)

where k is some constant of proportionality that is irrelevant to our analysis.

To fill in the crit factor, we have to take a moment to understand how critical hits work. We will assume for simplicity that the character's Crit Damage stat is 2x. (This stat is distinct from the weapon's Crit Damage stat). Thus the actual damage from a critical hit = Damage * 2 * (1 + Crit Damage). For example, the Revolver starts at 5 Damage and 0% Crit Damage, so critical hits do 5 * 2 * (1 + 0%) = 10 damage.

To work out the Crit factor in the above equation, we need to subtract and factor out the Damage (giving us just the bonus damage due to crits) and then multiply by the Crit Chance. This gives us

• Crit factor = Crit Chance * (2 * (1 + Crit Damage) - 1)

Putting it together, we get:

• DPS = k * Damage * Projectile Count * (1 + Projectile Bounces) * (1 + Crit Chance * (2 * (1 + Crit Damage) - 1))

To answer the question "which upgrade will increase your DPS the most?", we can ask a simpler question: "what weapon stats will result in any available common upgrade increasing DPS by exactly 10%?" (This will give us a Nash equilibrium of weapon upgrade strategies.)

Given that the Revolver has these upgrade values:


You can use the DPS formula above to verify that any upgrade will improve the DPS by 10% when the Revolver has the following stats:


The DPS Improvement Factor is straightforward to calculate when upgrading Damage, Projectile Count, or Projectile Bounces. It is equal to:

• Damage Upgrade / Current Damage
  
• Projectile Count Upgrade / Current Projectile Count
  
• Projectile Bounces Upgrade / (Current Projectile Bounces + 1)

For example, upgrading the Revolver's damage from 25 will yield a 2.5/25 = 10% DPS improvement, regardless of the Revolver's other stats. This aligns with our intuition that we get diminishing returns from each upgrade as the Revolver's damage scales up. Thus, if the Damage, Projectile Count, or Projectile Bounces is less than the values in the above table, then its upgrade will yield a DPS improvement greater than 10%.

Upgrading the Crit Chance and Crit Damage is more complicated though since each upgrade's effect on DPS depends on the current values of both Crit Chance and Crit Damage.

When you upgrade Crit Damage:

• 

When you upgrade Crit Chance:

• 

We can similarly see diminishing returns when either stat is upgraded in isolation. Thus we can conclude that our build is optimized when these stats have a Nash equilibrium, so we can simplify our lives by setting these equations equal to each other and solving:

• 

For the Revolver, this simplifies to Current Crit Chance = Current Crit Damage / 2 + 25%. As an example, if our Crit Damage is currently 100%, this tells us that we should upgrade Crit Chance until it is 1/2 + 25% = 75%.

While it is true that upgrading either of these stats in isolation yields diminishing returns, there is a bit of an oddity when they're in equilibrium at low values. The DPS Improvement Factor reaches a maximum of 10% when the Revolver's Crit Chance and Crit Damage are at 50%. This means that, until Crit Chance and Crit Damage reach 50%, upgrading these stats in equilibrium yields increasing returns. Thus it's not worth upgrading Crit Chance and Crit Damage at all until the other stats give less than 10% DPS improvement.

Putting this all together, we get the following table for the Revolver:


It is important to note that this analysis has several limitations, including:

• Charge shrine upgrades, items, and base stats of some characters can throw off the balance of these stats.
  
• This analysis does not consider the impact of rarity when selecting an upgrade. Optimizing for short-term gains does not always produce the best long-term outcomes.
  
• The equations assume that Crit Chance scales naturally beyond 100%. (E.g. at 200% every strike does the base damage plus double the bonus crit damage.) This may not be the case.
  
• The DPS calculation assumes that there are enough enemies to saturate the projectile count and bounces. A different strategy would benefit boss battles.